On their own, the \(N\)  constraints eqns.(REF ) lead to a rather simple dynamics; an isotropic diffusion that demonstrates no correlations among the particles. To go further towards a richer dynamics that exhibits such correlations, we require a device that allows for interdependence between the particles. This is achieved by introducing a global scalar function \(\phi (x)\)  (i.e. a function defined on the configuration space \(\mathbf {X}_{N}\) , rather than real space \(\mathbf {X}\) ), which we refer to as the drift potential and that mediates the inter-particle relationships in our system.Alternative formulations of ED (see e.g., [1]}[2]}) favor a different strategy, introducing some additional y-variables whose entropy \(S_{y}(x)\)  assumes the role normally reserved for the drift potential. However, these models run into some trouble, since entropy must necessarily be single-valued function, whereas the phase of the quantum state \(\Psi (x)\)  must, in fact, be multi-valued to accommodate, for example, states of non-zero angular momentum. For this reason we work exclusively with the drift potential \(\phi (x)\) .
